CMG Collaborative Research: Tempered stable models for preasymptotic pollutant transport in natural media

污染物通过天然含水层的传输通常在空间和时间尺度上表现出对大多数环境问题至关重要的预渐近或瞬时异常行为。所有相关尺度上复杂且通常不可预测的介质非均质性促使非局部运输理论的应用。这项工作将发展回火稳定模型，该模型通过调整分形幂定律来推广标准的非局部输运理论，以模拟预渐近输运并揭示先前遗漏的真实世界弥散的本质。主要成果包括：(1)一种新的基于回火幂定律的非局域输运理论和模型，可以有效地模拟瞬时异常扩散；(2)自然非均质介质的可观测统计数据与系统的蒙特卡罗研究建立的模型参数之间的定量联系；(3)一套方便的开放源代码的软件套件，用于求解和应用该模型。这项合作研究还将通过使用历史示踪剂数据和经过充分研究的含水层信息来测试模型、解算器和模型的可预测性。仔细考虑模型组件的物理意义以及与含水层统计属性的联系，将确保所得到的模型不仅限于曲线拟合应用。准确预测污染物在真实含水层中的迁移对于地下水保护和清理至关重要。拟议的工作将发展适当的运输理论，并建立有效的建模组件来解决这个问题。因此，本研究具有很强的理论性和应用性。特别是，拟议的工作更准确地反映了真实含水层材料中分数微积分和幂定律统计之间的潜在联系。PI团队包括数学家和水文学家，在尖端研究方面形成了跨学科合作。

Contaminant transport through natural aquifers typically exhibits pre-asymptotic or transient anomalous behavior on the space and time scale critical to most environmental concerns. Complex and usually unpredictable medium heterogeneity at all relevant scales motivates the application of non-local transport theories. The proposed work will develop tempered stable models, which generalize standard non-local transport theories by adjusting fractal power-laws, to simulate pre-asymptotic transport and reveal the nature of real-world dispersion missed previously. There will be three major outcomes, including (1) a novel non-local transport theory and model based on tempered power laws that can efficiently simulate transient anomalous diffusion, (2) a quantitative linkage between the observable statistics of natural heterogeneous media and the model parameters built by a systematic Monte Carlo study, and (3) a convenient software suite with open source codes that solve and apply the model. This collaborative research will also test the model, the solver and the model predictability, by using historical tracer data and well-studied aquifer information. A careful consideration of the physical meaning of model components, and connections to statistical aquifer properties, will ensure that the resulting model is not limited to curve fitting applications.Accurate prediction of contaminant migration in real-world aquifers is critical to groundwater protection and cleanup. The proposed work will develop appropriate transport theory and build effective modeling components to address this problem. Hence this research is both highly theoretical and applied. In particular, the proposed work more accurately represents the underlying link between fractional calculus and power-law statistics in real aquifer material. The PI team includes mathematicians and hydrologists, forming interdisciplinary cooperation in cutting edge research.